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A355498 a(n) = A000217(A033676(n)) * A000217(A033677(n)). 0
1, 3, 6, 9, 15, 18, 28, 30, 36, 45, 66, 60, 91, 84, 90, 100, 153, 126, 190, 150, 168, 198, 276, 210, 225, 273, 270, 280, 435, 315, 496, 360, 396, 459, 420, 441, 703, 570, 546, 540, 861, 588, 946, 660, 675, 828, 1128, 756, 784, 825, 918, 910, 1431, 945, 990, 1008, 1140, 1305, 1770 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
When n squares are arranged in a rectangular grid which is as nearly square as possible, a(n) represents the count of rectangles in the grid. The whole grid itself must be a rectangle too.
LINKS
EXAMPLE
For n=10, the grid as nearly square as possible is 2*5. Thus a(10)=3*15=45 is the number of rectangles in this grid.
MATHEMATICA
Table[(# (# + 1)/2) &[
First[Select[Divisors[n], # >= Sqrt[n] &]]] (# (# + 1)/2) &[
Last[Select[Divisors[n], # <= Sqrt[n] &]]], {n, 80}]
PROG
(PARI) t(n) = n*(n+1)/2; \\ A000217
largdiv(n) = if(n<2, 1, my(d=divisors(n)); d[(length(d)+1)\2]); \\ A033676
a(n) = my(d=largdiv(n)); t(d)*t(n/d); \\ Michel Marcus, Jul 18 2022
CROSSREFS
Sequence in context: A259728 A000741 A133205 * A049991 A368611 A143981
KEYWORD
nonn
AUTHOR
Steven Lu, Jul 04 2022
STATUS
approved

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Last modified April 21 03:36 EDT 2024. Contains 371850 sequences. (Running on oeis4.)